A vessel construction which provides steady continuous discharge of liquids therefrom when the vessel is tilted to a discharge position, and a sharp cut-off of flow when the vessel is return tilted to a normal upright condition, has long been an objective of both vessel manufacturers and users alike. The need for such a construction is particularly acute in connection with liquids of a thick and viscous nature, such as maple syrup. However, the problem also is common to highly fluid liquids, such as tea when poured from a tea pot. When dribble or dripping occurs a portion of the liquid is wasted, the post-pouring dribble or dripped liquid may fall onto a surface which is not intended to receive it such as the user's clothing or the floor, the vessel takes on an unsightly appearance which can become worse as time passes with the entrapment of dirt therein, and an unsanitary condition can develop over time. Proposals have been made to eliminate this problem but it is believed that all such proposals have one or more disadvantages which has prevented any construction of choice to evolve. Typical of the attempts which have been made to develop such a construction which have not gone into widespread use (if, indeed, into any commercial use) is the construction shown in the Reller et. al. U.S. Pat. No. 3,145,887 in which a ledge shoulder located just behind the distal end or edge of the vessel is employed as a dam to provide a dripless rim. While such structure may be effective to reduce or even prevent dripping, the dam generates a sharp edge or protrusion which is unpleasant to the sensitive tissues of the mouth and thus, for this reason, it is believed that such a construction has not gone into significant, if any, use.